We examined the nucleation and grain growth kinetics of a nano icosahedral phase formed as a primary phase in the Zr65Al7.5Ni10Cu17.5-xPdx (x = 5, 10 and 17.5) glassy alloys by differential scanning calorimetry and transmission electron microscopy. The nano icosahedral grains are distributed homogeneously, indicating the homogeneous nucleation mode. The grain growth rate of the icosahedral phase is nearly constant at the initial stage and much lower than that of the cubic Zr2Ni phase in the Zr65Al7.5Ni10Cu17.5 glassy alloy. The growth rate decreases with increasing Pd content. It is (4.5±0.4) × 10-9 ms-1 at x = 5 and decreases to (8.3 ± 0.8) × 10-10 ms-1 at x = 17.5. The homogeneous nucleation rate at crystallization temperature, Tx, changes drastically with Pd content, and is (1.1 ± 0.3) × 1020 m-3s-1 in the Zr65Al7.5Ni10Cu7.5Pd10 glass, which is approximately 102 times higher than that in the Zr65Al7.5Ni10Cu12.5Pd5 glass and 104 times higher than that of the Zr2Ni phase in the Zr65Al7.5Ni10Cu17.5 glass. Thus, it is clarified that with increasing the Pd content, the nucleation rate of the primary phase increases significantly and its growth rate decreases. The addition of Pd is effective for the increase in the number of nucleation sites and the suppression of grain growth. The formation of the nano icosahedral phase by the addition of Pd implies the existence of icosahedral short-range order in the glassy state of the Zr-Al-Ni-Cu alloy.